1. Field of the Invention
The present invention relates to a threshold matrix and a method of generating such a threshold matrix, for generating a screen which is called an FM screen or a stochastic screen for converting a continuous-tone image into a dot pattern representative of a binary image. More particularly, the present invention relates to a threshold matrix, a method of generating such a threshold matrix, and a method of reproducing a color image that are suitable for use in a printing-related apparatus (output system) such as a filmsetter, a platesetter, a CTP (Computer To Plate) apparatus, a CTC (Computer To Cylinder) apparatus, a DDCP (Direct Digital Color Proof) system, etc., an ink jet printer, or an electrophotographic printer.
2. Description of the Related Art
Heretofore, so-called AM (Amplitude Modulation) screens characterized by screen ruling, screen angle, and dot shape, and FM (Frequency Modulation) screens have been used in the art of printing.
A process of generating a threshold matrix for FM screens is disclosed in Japanese Laid-Open Patent Publication No. 8-265566.
According to the disclosed process, an array of elements of a threshold matrix, i.e., an array of thresholds, is generated in an ascending order or a descending order by determining threshold positions such that the position of an already determined threshold is spaced the greatest distance from the position of a threshold to be newly determined. The dot pattern of a binary image that is generated using the threshold matrix thus produced has dots which are not localized. Even when a dot pattern is generated using a plurality of such threshold matrixes that are juxtaposed, the dot pattern does not suffer a periodic pattern produced by the repetition of threshold matrixes.
A plurality of patent documents given below are relevant to the generation of a threshold matrix.
Japanese Patent No. 3400316 discloses a method of correcting halftone image data by extracting a pixel having a weakest low-frequency component of a certain dot pattern, from white pixels (unblackened pixels), and a pixel having a strongest low-frequency component of the dot pattern, from blackened pixels, and switching around the extracted white and blackened pixels. Thus, the dot pattern is intended to be smoothed or leveled.
Japanese Laid-Open Patent Publication No. 2001-292317 reveals a process of determining threshold positions in a threshold matrix such that a next blackened pixel is assigned to a position having a weakest low-frequency component of the threshold matrix.
Japanese Laid-Open Patent Publication No. 2002-368995 shows a process of determining threshold positions in a threshold matrix such that when an array of thresholds in the threshold matrix has been determined up to a certain gradation and a threshold position for a next gradation is to be determined, blackened pixels are assigned to positions for not strengthening a low-frequency component.
Japanese Laid-Open Patent Publication No. 2002-369005 discloses a process of generating a threshold matrix according to the process shown in Japanese Patent No. 3400316, Japanese Laid-Open Patent Publication No. 2001-292317 and Japanese Laid-Open Patent Publication No. 2002-368995, based on an ideal dot pattern at a certain gradation which is given.
When an FM screen is used for offset printing, it causes shortcomings in that the quality of printed images suffers some grainness. FM screens also cause disadvantages in that a dot gain tends to become large and images are reproduced unstably when images are printed, or when films are output in an intermediate printing process, or when a printing plate is output by a CTP apparatus.
According to the conventional FM screening process, when a dot size is determined to be the size of a dot made up of one pixel or a dot made up of four pixels according to a 1 (1×1)-pixel FM screen or a 4 (2×2)-pixel FM screen, an array of thresholds of a threshold matrix is determined by an algorithm for generating FM screens, thus determining an output quality, and only the dot size serves as a parameter for determining the quality of FM screens. For example, if a dot size is determined to be a 3×3-pixel FM screen dot size with respect to an output system which is incapable of stably reproducing 2×2-pixel FM screen dots for highlight areas, then the resolution (referred to as pattern frequency or pattern resolution) for intermediate tones is lowered, resulting in a reduction in the quality of images.
FIG. 21 of the accompanying drawings shows a conventional dot pattern 1 in a highlight area where the dot percentage of a 2×2-pixel FM screen is 5%, a conventional dot pattern 2 in an intermediate tone area where the dot percentage of the 2×2-pixel FM screen is 50%, a conventional dot pattern 3 in a highlight area where the dot percentage of a 3×3-pixel FM screen is 5%, and a conventional dot pattern 4 in an intermediate tone area where the dot percentage of the 3×3-pixel FM screen is 50%.
FIG. 22 of the accompanying drawings shows a power spectrum generated when the dot pattern 2 of the 2×2-pixel FM screened shown in FIG. 21 is FFTed (Fast-Fourier-Transformed), and FIG. 23 of the accompanying drawings shows a power spectrum generated when the dot pattern 4 of the 3×3-pixel FM screen shown in FIG. 21 is FFTed.
In FIG. 21, at the dot percentage of 50% in the intermediate tone area, the dot pattern 2 of the 2×2-pixel FM screen suffers less grainness than the dot pattern 4 of the 3×3-pixel FM screen, but has the dot percentage less reproducible in the printed image. On the other hand, at the dot percentage of 50% in the intermediate tone area, the dot pattern 4 of the 3×3-pixel FM screen has a pattern frequency 6 of about 13 c/mm which is lower than the pattern frequency 5 of about 20 c/mm of the dot pattern 2 of the 2×2-pixel FM screen. The pattern frequencies 5, 6 which are of peak values are also called a peak spatial frequency fpeak.
The output resolution of an output system such as an imagesetter, a CTP apparatus, etc. (the output resolution of an output system will hereinafter be referred to as output resolution R) is set to 2540 pixels/inch=100 pixels/mm or 2400 pixels/inch=94.488 pixels/mm, for example. With those settings, the dot size of the 1×1 pixel FM screen is 10 μm×10 μm (10.6 μm×10.6 μm), and the dot size of the 2×2 pixel FM screen is 20 μm×20 μm (21.2 μm×21.2 μm). In this description, the output resolution R is different from the pattern frequencies 5, 6 of the dot patterns 2, 4 shown in FIGS. 22, 23.
As described above, only the dot size is a parameter for determining the quality of conventional FM screens.
It is considered in this connection that the conventional FM screens have a greater periphery length (to be described in detail later on) than the AM screens at the same dot percentage.